The highlight of Burr's tenure as President of the Senate (one of his few official duties as Vice President) was the Senate's first impeachment trial, of Supreme Court Justice Samuel Chase. In 1804, the last full year of his single term as Vice President, Burr killed his political rival Alexander Hamilton in a famous duel. Burr was never tried for the illegal duel, and all charges against him were eventually dropped, but Hamilton's death ended Burr's political career.

After leaving Washington, Burr traveled west seeking new opportunities, both economic and political. His activities eventually led to his arrest on charges of treason in 1807. Although the subsequent trial resulted in acquittal, Burr's western schemes left him with large debts and few influential friends. In a final quest for grand opportunities, he left the United States for Europe. He remained overseas until 1812, when he returned to the United States to practice law in New York City. There he spent the remainder of his life in relative obscurity.